Introduction to Nonextensive Statistical Mechanics

This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics.

Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the BG theory, one of the greatest monuments of contemporary physics, exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced.

Since the first edition release thirteen years ago, there has been a vast amount of new results in the field, all of which have been incorporated in this comprehensive second edition. Heavily revised and updated with new sections and figures, the second edition remains the go-to text on the subject.

A pedagogical introduction to the BG theory concepts and their generalizations – nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, generalization of the standard CLT’s, complex networks, among others – is presented in this book, as well as a selection of paradigmatic applications in various sciences together with diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics.

“This book provides an introduction into the foundations of nonextensive statistical mechanics and an overview of its numerous applications. … the author answers to some common critiques of the theory in the form of question-answer, which also serves a good summary of the key ideas developed throughout the book” (Artem Sapozhniko, zbMATH 1522.82002, 2023)

Constantino Tsallis is a physicist in the area of statistical mechanics, Emeritus Professor at the Department of Theoretical Physics of the Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil, and founding member of the National Institute of Science and Technology for Complex Systems, Brazil. He is also External Faculty Fellow of the Santa Fe Institute, New Mexico, USA, External Faculty of the Complexity Science Hub Vienna, Austria, and Professor at the Dottorato in Sistemi Complessi per le Scienze Fisiche, Socio-economiche e della Vita of the University of Catania. He is Docteur d´État ès Sciences Physiques of the University of Paris-France (1974). He worked in a variety of theoretical subjects in the areas of critical phenomena, chaos and nonlinear dynamics, economics, cognitive psychology, immunology, population evolution, among others. For the last three decades, he has focused on the entropy and the foundations of statistical mechanics, as well as on some of their scientific and technological applications. Indeed, he proposed in 1988 a generalization of Boltzmann-Gibbs entropy and statistical mechanics. This generalization is presently being actively studied around the world; a regularly updated bibliography containing more than 8,500 directly related articles by over 15,000 scientists from all over the world is available online.

Prof. Tsallis' contributions have received over 22,000 citations at the ISI Web of Science, 6,000 of them for his 1988 paper, which currently makes him one among the most cited scientists of all times in Latin America. He has received many distinctions (Guggenheim Foundation Award, Mexico Prize for Science and Technology, Rio de Janeiro Prize of Science and Technology, among many others), and has been given the title of Doctor Honoris Causa by Universities from Argentina (Cordoba), Brazil (Maringa and Natal) and Greece (the Thessaloniki Aristotelian University). He was awarded the highest distinction of the Academyof Athens (originally founded by Plato). He is member of the Academy of Sciences of Brazil, of the Academy of Economical, Political and Social Sciences of Brazil, and of the Academy of Sciences of Latin America. He is Honorary Editor of Physica A, and has supervised close to 40 Doctor and Master Thesis. He has given regular undergraduate and graduate courses in Physics in Brazil, Argentina, USA, France, Italy and Germany, and has delivered over 1,000 invited lectures around the world. In 2005 and 2006, he did basic research at the Santa Fe Institute, New Mexico, where he coauthored several papers with Murray Gell-Mann.